<p>This study utilizes the symplectic superposition method to examine the natural vibration behavior of rectangular thin plates made of sigmoid functionally graded materials (S-FGM) supported by a Winkler–Pasternak foundation, and the free vibration frequencies and modes of the S-FGM rectangular thin plates with fully clamped are emphatically explored. Firstly, the free vibration equation of an S-FGM rectangular thin plate on the Winkler–Pasternak foundation is transformed into Hamiltonian canonical equations. Through boundary condition analysis, the free vibration problem of a fully clamped plate is decomposed into two subproblems with simply supported on two opposite edges, and their general solutions are derived. The symplectic superposition solution for clamped S-FGM rectangular thin plates on the Winkler–Pasternak foundation is derived through the superposition of the two subproblems’ general solutions. Then, based on the symplectic superposition solution obtained, the present work researches the vibration characteristics of such plates. The vibration frequencies under different length-width ratios, material volume fractions, and foundation parameter combinations are investigated. The vibration characteristics of S-FGM rectangular thin plates on Winkler–Pasternak foundation are studied, including numerical simulation and graphical presentation of its first three modal shapes. Additionally, a comprehensive convergence analysis is conducted for fully clamped rectangular thin plates supported by the Winkler–Pasternak foundation model. In this study, the analytical solution for the vibration problem of fully clamped S-FGM rectangular thin plates on Winkler–Pasternak elastic foundations is obtained for the first time, which extends the scope of the analytical solutions for the vibration problems of functionally graded materials.</p>